Theridiidae is a very large family of spiders (Wikipedia tells me there are over 2200 species). One famous example is the Hawiian happy face spider, which is cute AND has an interesting evolutionary history (it is only found in certain locations along the Hawaiian chain of islands).
The most obvious Theridiid species from Australia is Latrodectus hasseltii, the Redback spider. Interestingly, I have only ever seen Redbacks on man-made objects, never on plants or in bushland. This really makes me wonder what their native habitat is!
There are also many other Theridiid spiders which are very common in urban backyards. I’ve found 20 different species so far, but most people wouldn’t even know they were there.
The most common comes from the genus Anelosimus. I’ve found these guys in most of the gardens I’ve surveyed, but you don’t notice them because they are very small and live curled up in leaves (sorry about the photo quality, they are really small!).
Another very common (and I think very pretty) group of spiders come from the genus Theridon. They have a multicolored, triangular abdomen and although they make a small web they are normally found hiding in their “retreat” between small leaves.
And now for some of the less common species that I’ve found. I’ve only found one or two of each of these so far and I don’t know anything about their ecology unfortunately.
These three below are from the Genus Episinus, which have a characteristically interesting abdomen shape.
And here is a selection of some of the other species I’ve found, both in bushland and in back gardens.
Finally, my favorite Theridiid species so far. I’m pretty sure it belongs to the Phoroncidiinae genus, but the Theridiidae are so diverse sometimes it’s hard to tell. The photos really don’t do it justice, but it is a very cute little spider with a very pointed abdomen and eyes which are raised up from the cephalothorax.